Question

以知N分之M=5分之3,求（M+N分之M）+（M—N分之M）—（M平方—N平方分之N平方）的值

Answer 1

m/n=3/5 则n/m=5/3

m/(m+n)+m/(m-n)-[n^2/(m^2-n^2)]

=[m(m-n)+m(m+n)-n^2]/(m^2-n^2)

=(2m^2-n^2)/(m^2-n^2)

=1+m^2/(m^2-n^2)

=1+1/[1-(n/m)^2]

=1+1/(1-25/9)

=1+9/16

=25/16